1. Which will have a longer period of oscillation T, a mass of 0.6 kg hanging fr
ID: 1352429 • Letter: 1
Question
1. Which will have a longer period of oscillation T, a mass of 0.6 kg hanging from the spring, or a mass of 0.7 kg (same spring)?
2. Sketch a graph of x vs. t, from Eq. 2, for the two cases ? = 0 and ? = ?/2.
3. Sketch graphs of v vs. t and a vs. t for the two cases drawn in problem 2.
4. According to Eq. 2, x varies from (-A) to (+A). At which point(s) in its cycle does the mass have its greatest speed? (a) x = + A (b) x = 0 (c) same at all points.
5. At which of the previous points does the mass have its greatest potential energy?
Introduction: In this experiment you will measur thespring constant using two dferent methods and compar your results. Hooke's law for a spring states that: F=-kx, where x is the displacement of the spring from equilibrium, F is the force exerted by the spring, and k is the spring constant. The negative sign just means that the restoring force is opposite in direction to the displacement. If a spring obeys Hooke's law, then a mass hung from the end of the spring will undergo simple harmonic motion when displaced from equilibrium and released. That is, x = Acos (ot+ ), where A is the amplitude of oscillation (maximum displacement from equilibrium), is the angular frequency in rad/s, and is a phase angle that depends on when timing starts, as related to the frequency in hertz (f) and the period (T) by -2zf-22T By substituting Eq. (2) into Eq. ( 1 ) and using Newton's 2nd law of motion, it can be shown that , and T = 27,1 m Thus, k can be measured statically using Eq. (1) or dynamically using Eq (3).Explanation / Answer
1) the higher mass will have a higher time of oscillation
2) the graph will be a cosine curve for phase angle 0 and it will be a sine curve for phase angle 90 degrees.
3) the graph will be a sine curve for phase angle 0 and it will be a cosine curve for phase angle 90 degrees.
4) the mass will have the greatest speed at x= 0
5) it will have the greatest potential energy at x = +A or -A
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